Trigonometry as 12.3.5

8/4/2019 Trigonometry as 12.3.5

1/15

TrigonometryTrigonometry

A S 12.3.5


2/15

h

o

ehypoteneus

oppositeAsin =

ha

hypotenuseadjacentAcos =

a

o

adjacent

oppositeAtan =

In a 900

triangle:h2 = o2 + a2

Pythagoras

The ratios of the sidesare defined as:

adjacent

hy

potenuse

oppos

it

e

A

Triangle ActionTriangle Action

sin B = 3/5

e.g. 5

4

3

B


3/15

Lets ReviseLets Revise

Calculate the unknown side:

For 500 angle;givenadjacent;need opposite

For 400 angle;given opposite;

needhypotenusetan 50 = y/9

y = 9 . tan 50

10,73

sin 40 = 8/x

x = 8/sin 40

12,45

5009

y

400

x8


4/15

Calculate the unknown angle:

For angle A;given adjacent;given

hypotenusecos A = 8/17


5/15

Morgan Point is 6

km east and 4 kmnorth of CapePoint. Cape Point

Morgan

Point

4km

6km

N

Steve sails directly fromCape Point to MorganPoint. What is his

bearing?

A

tan A = 6/4


6/15

IfIf not 90not 9000

Use sine rule:

c

C

b

B

a

A sinsinsin= B C

A

a

bc

Find the length of EF.

EF

60sin

13

55sin=

60sinEF 13.55sin. =

EF= cm7413,

550

600

13cm

D

E F

e.g.

1

Always makesure your angleis opposite theside to form a

ratio.


7/15

A

B C460

19cm

31cm

Determine


8/15

Use cosine rule:

Calculate BC if in ABC,


9/15

ab

cbaCosC

2

222 =

01,34C

8cm

12

cm

7cmA

B

C

c

ab

8122

7812222

=CosC

Calculate


10/15

Area rule: (If height is not given.)3

B C

A

a

bcArea ABC = a b sin CorArea ABC = a c sin B orArea ABC = b c sin A

The angle used always lies between two sides.i.e.


11/15

A space shuttle is tied

down by two 120 m longchains. The angle ofelevation is 65,380.Calculate the distance

between the tie downpoints on the ground.

ApplicationsApplications

distance

65,38

120120

S


12/15

P shows a point where

a penalty kick is takenfrom in a rugby match.The distance betweenthe posts is 5,5m.


13/15

A and B are two points on oppositessides of tower CD. AB = 170m and

angles of elevation from A and B are41,50 and 58,10 respectively.Find the size of


14/15

630kmN(Nelspruit

P(Polokwane)

230

M(Bloemfontein)

675

km

The navigationtriangle shows the

distances to fly fromBloemfontein to Pand N.Determine the distance

from Nelspruit toPolokwane.

NP2 = 6752 + 6302 2x675x630xcos230

= 69635NP = 263,89 km

Calculate the area enclosed by thenavigation triangle.Area = x 675 x 630 x sin230

= 83 079,21 km2

4.N


15/15

Mr Ndaki bought farm land that has atriangular shape. The area A of the farm =

1024 m2

. The length of side PR= 59 m and

Trigonometry as 12.3.5

Documents

Transcript of Trigonometry as 12.3.5